/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date:        15. February 2012
* $Revision: 	V1.1.0
*
* Project: 	    CMSIS DSP Library
* Title:		arm_cos_q31.c
*
* Description:	Fast cosine calculation for Q31 values.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.1.0 2012/02/15
*    Updated with more optimizations, bug fixes and minor API changes.
*
* Version 1.0.10 2011/7/15
*    Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
*    Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
*    Documentation updated.
*
* Version 1.0.1 2010/10/05
*    Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
*    Production release and review comments incorporated.
* -------------------------------------------------------------------- */

#include "arm_math.h"

/**
 * @ingroup groupFastMath
 */

/**
* @addtogroup cos
* @{
*/

/**
 * \par
 * Table Values are in Q31(1.31 Fixed point format) and generation is done in three steps
 * First Generate cos values in floating point:
 * tableSize = 256;
 * <pre>for(n = -1; n < (tableSize + 1); n++)
 * {
 *	cosTable[n+1]= cos(2*pi*n/tableSize);
 * } </pre>
 * where pi value is  3.14159265358979
 * \par
 * Secondly Convert Floating point to Q31(Fixed point):
 *	(cosTable[i] * pow(2, 31))
 * \par
 * Finally Rounding to nearest integer is done
 * 	cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);
 */


static const q31_t cosTableQ31[259] = {
	0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f,
	0x7f0991c4, 0x7e9d55fc,
	0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b,
	0x798a23b1, 0x78848414,
	0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6,
	0x6f5f02b2, 0x6dca0d14,
	0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac,
	0x60ec3830, 0x5ed77c8a,
	0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94,
	0x4ebfe8a5, 0x4c3fdff4,
	0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70,
	0x398cdd32, 0x36ba2014,
	0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e,
	0x2223a4c5, 0x1f19f97b,
	0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e,
	0x96a9049, 0x647d97c,
	0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5,
	0xed37ef91,
	0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2,
	0xd7d946d8, 0xd4e0cb15,
	0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590,
	0xc0e8b648, 0xbe31e19b,
	0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c,
	0xac64d510, 0xaa0a5b2e,
	0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54,
	0x9b1776da, 0x99307ee0,
	0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a,
	0x8daad37b, 0x8c4a142f,
	0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5,
	0x84a2fc62, 0x83d60412,
	0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971,
	0x8058c94c, 0x80277872,
	0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971,
	0x80f66e3c, 0x8162aa04,
	0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5,
	0x8675dc4f, 0x877b7bec,
	0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a,
	0x90a0fd4e, 0x9235f2ec,
	0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54,
	0x9f13c7d0, 0xa1288376,
	0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c,
	0xb140175b, 0xb3c0200c,
	0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590,
	0xc67322ce, 0xc945dfec,
	0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2,
	0xdddc5b3b, 0xe0e60685,
	0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2,
	0xf6956fb7, 0xf9b82684,
	0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b,
	0x12c8106f,
	0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e,
	0x2826b928, 0x2b1f34eb,
	0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70,
	0x3f1749b8, 0x41ce1e65,
	0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94,
	0x539b2af0, 0x55f5a4d2,
	0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac,
	0x64e88926, 0x66cf8120,
	0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6,
	0x72552c85, 0x73b5ebd1,
	0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b,
	0x7b5d039e, 0x7c29fbee,
	0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f,
	0x7fa736b4, 0x7fd8878e,
	0x7ff62182, 0x7fffffff, 0x7ff62182
};

/**
 * @brief Fast approximation to the trigonometric cosine function for Q31 data.
 * @param[in] x Scaled input value in radians.
 * @return  cos(x).
 *
 * The Q31 input value is in the range [0 +0.9999] and is mapped to a radian value in the range [0 2*pi), Here range excludes 2*pi.
 */

q31_t arm_cos_q31(
    q31_t x)
{
	q31_t cosVal, in, in2;                         /* Temporary variables for input, output */
	q31_t wa, wb, wc, wd;                          /* Cubic interpolation coefficients */
	q31_t a, b, c, d;                              /* Four nearest output values */
	q31_t* tablePtr;                               /* Pointer to table */
	q31_t fract, fractCube, fractSquare;           /* Temporary values for fractional values */
	q31_t oneBy6 = 0x15555555;                     /* Fixed point value of 1/6 */
	q31_t tableSpacing = TABLE_SPACING_Q31;        /* Table spacing */
	q31_t temp;                                    /* Temporary variable for intermediate process */
	int32_t index;                                 /* Index variable */

	in = x;

	/* Calculate the nearest index */
	index = in / tableSpacing;

	/* Calculate the nearest value of input */
	in2 = ((q31_t) index) * tableSpacing;

	/* Calculation of fractional value */
	fract = (in - in2) << 8;

	/* fractSquare = fract * fract */
	fractSquare = ((q31_t)(((q63_t) fract * fract) >> 32));
	fractSquare = fractSquare << 1;

	/* fractCube = fract * fract * fract */
	fractCube = ((q31_t)(((q63_t) fractSquare * fract) >> 32));
	fractCube = fractCube << 1;

	/* Checking min and max index of table */
	if(index < 0) {
		index = 0;
	} else if(index > 256) {
		index = 256;
	}

	/* Initialise table pointer */
	tablePtr = (q31_t*) & cosTableQ31[index];

	/* Cubic interpolation process */
	/* Calculation of wa */
	/* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */
	wa = ((q31_t)(((q63_t) oneBy6 * fractCube) >> 32));
	temp = 0x2AAAAAAA;
	wa = (q31_t)((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32);
	wa = -(wa << 1u);
	wa += (fractSquare >> 1u);

	/* Read first nearest value of output from the cos table */
	a = *tablePtr++;

	/* cosVal = a*wa */
	cosVal = ((q31_t)(((q63_t) a * wa) >> 32));

	/* q31(1.31) Fixed point value of 1 */
	temp = 0x7FFFFFFF;

	/* Calculation of wb */
	wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp;
	/* Read second nearest value of output from the cos table */
	b = *tablePtr++;

	/*      cosVal += b*wb */
	cosVal = (q31_t)((((q63_t) cosVal << 32) + ((q63_t) b * (wb))) >> 32);

	/* Calculation of wc */
	wc = -fractCube + fractSquare;
	wc = (wc >> 1u) + fract;
	/* Read third nearest values of output value from the cos table */
	c = *tablePtr++;

	/*      cosVal += c*wc */
	cosVal = (q31_t)((((q63_t) cosVal << 32) + ((q63_t) c * (wc))) >> 32);

	/* Calculation of wd */
	/* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
	fractCube = fractCube - fract;
	wd = ((q31_t)(((q63_t) oneBy6 * fractCube) >> 32));
	wd = (wd << 1u);

	/* Read fourth nearest value of output from the cos table */
	d = *tablePtr++;

	/* cosVal += d*wd; */
	cosVal = (q31_t)((((q63_t) cosVal << 32) + ((q63_t) d * (wd))) >> 32);


	/* convert cosVal in 2.30 format to 1.31 format */
	return (__QADD(cosVal, cosVal));

}

/**
 * @} end of cos group
 */
